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固体力学学报(英文版)
固体力学学报(英文版)

余寿文

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0894-9166

amss@mail.hust.edu.cn

027-87543737

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武汉市珞瑜路1037号

固体力学学报(英文版)/Journal Acta Mechanica Solida SinicaCSCD北大核心EISCI
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    Preface to the"Theory and Applications of Flexoelectricity"Special Issue of Acta Mechanica Solida Sinica

    Qian DengYue ZhengShengping Shen
    519-520页

    Enhanced Flexoelectricity in Barium Titanate-Cellulose Composite Thin Films

    Wensi XingHongyu CaoXin ZhangXu Liang...
    521-527页
    查看更多>>摘要:Biopolymers,the potential flexoelectric materials,are environment-friendly,degradable,lightweight,cost-effective,and pos-sess remarkable processing properties catering to the requirements of advanced devices.However,the flexoelectric coefficient of biopolymers is normally much weaker than that of ceramic materials,limiting their potential applications for designing high-performance green electromechanical coupling devices.To improve the flexoelectric response in biopolymers,we com-posited barium titanate(BTO)with 2,2,6,6-tetramethylpiperidine-l-oxyl-oxidized cellulose nanofibrils(TOCNF)to enhance the flexoelectric response of TOCNF.Owing to the high permittivity and flexoelectric effect of BTO,the relative dielectric constant and flexoelectric coefficient of 33.3 wt%BTO-TOCNF films reached 30.94@1 kHz and 50.05±1.88 nC/m@1 Hz,which were almost 172 times and 27 times higher than those of TOCNF,respectively.The composite thin film contains high dielectric constant and flexoelectric coefficient,as well as excellent flexibility.Our study provided a straightforward and efficient method for improving the flexoelectric effect of biopolymers,and demonstrated its great potential applications in flexoelectric-based devices.

    Giant Flexoelectric Effect in Snapping Surfaces Enhanced by Graded Stiffness

    Chuo Zhao
    528-540页
    查看更多>>摘要:Flexoelectricity is present in nonuniformly deformed dielectric materials and has size-dependent properties,making it useful for microelectromechanical systems.Flexoelectricity is small compared to piezoelectricity;therefore,producing a large-scale flexoelectric effect is of great interest.In this paper,we explore a way to enhance the flexoelectric effect by utilizing the snap-through instability and a stiffness gradient present along the length of a curved dielectric plate.To analyze the effect of stiffness profiles on the plate,we employ numerical parameter continuation.Our analysis reveals a nonlinear relationship between the effective electromechanical coupling coefficient and the gradient of Young's modulus.Moreover,we demonstrate that the quadratic profile is more advantageous than the linear profile.For a dielectric plate with a quadratic profile and a modulus gradient of-0.9,the effective coefficient can reach as high as 15.74 pC/N,which is over three times the conventional coupling coefficient of piezoelectric material.This paper contributes to our understanding of the amplification of flexoelectric effects by harnessing snapping surfaces and stiffness gradient design.

    Enhanced Flexoelectric Response from Functionally Gradient Electrets Undergoing Crumpling Deformation

    Jianhua MaJinrui XuJun LiBinglei Wang...
    541-554页
    查看更多>>摘要:Non-uniform deformation of the dielectric subjected to external forces can induce the flexoelectric effect,a phenomenon that couples electrical polarization to strain gradients.However,limited by the size effects,flexoelectricity is not significant at the macroscale and only becomes catchable at the microscale and nanoscale.In recent work,we obtained a considerable flexoelectric-like response by crumpling the dielectric embedded with charges,i.e.,the electret,which significantly improved the flexoelectric effect at the macroscale.In this work,we further optimize the macroscopic performance of the flexoelectric response by applying gradient treatment to the electret films.Specifically,we analytically derive the electromechanical coupling of crumpled electret films with gradients of different thicknesses,charge densities,and Young's moduli as key design variables.It is shown that the gradient-oriented electret film can be tuned to nearly five times that of a uniform electret film.

    New Insight into the Flexoelectricity in the View of Mechanics of Materials:Prismatic Beams Subjected to Bending

    Xu YangLingling ChenShengyou Yang
    555-569页
    查看更多>>摘要:Flexoelectricity is a fascinating electromechanical phenomenon that occurs in non-homogeneously deformed dielectric mate-rials.Unlike piezoelectricity,the flexoelectric effect is highly dependent on both the material scale and the deformation gradient.Although several theoretical models have been proposed to explain the mechanism of flexoelectricity,these models can be rather complicated for those who are interested in studying the topic.This paper aims to simplify the understanding of flexoelectricity by focusing on the bending behavior of a prismatic dielectric beam from a mechanics of material perspective.We avoid using complicated mathematical formulations based on continuum mechanics,including advanced tensor algebra and calculus of variations.Our formulation clearly explains how inhomogeneous deformations and material size affect the electromechanical coupling,changing the effective bending stiffness,deflection,and rotation angles of a bending beam.We hope this paper can help undergraduate students and researchers,who are unfamiliar with the electromechanical coupling in flexoelectricity,to develop an understanding of this phenomenon and encourage further research in this area.

    Strain Gradient Finite Element Formulation of Flexoelectricity in Ferroelectric Material Based on Phase-Field Method

    Shuai WangHengchang SuMin YiLi-Hua Shao...
    570-579页
    查看更多>>摘要:Flexoelectricity is a two-way coupling effect between the strain gradient and electric field that exists in all dielectrics,regardless of point group symmetry.However,the high-order derivatives of displacements involved in the strain gradient pose challenges in solving electromechanical coupling problems incorporating the flexoelectric effect.In this study,we formulate a phase-field model for ferroelectric materials considering the flexoelectric effect.A four-node quadrilateral element with 20 degrees of freedom is constructed without introducing high-order shape functions.The microstructure evolution of domains is described by an independent order parameter,namely the spontaneous polarization governed by the time-dependent Ginzburg-Landau theory.The model is developed based on a thermodynamic framework,in which a set of microforces is introduced to construct the constitutive relation and evolution equation.For the flexoelectric part of electric enthalpy,the strain gradient is determined by interpolating the mechanical strain at the node via the values of Gaussian integration points in the isoparametric space.The model is shown to be capable of reproducing the classic analytical solution of dielectric materials incorporating the flexoelectric contribution.The model is verified by duplicating some typical phenomena in flexoelectricity in cylindrical tubes and truncated pyramids.A comparison is made between the polarization distribution in dielectrics and ferroelectrics.The model can reproduce the solution to the boundary value problem of the cylindrical flexoelectric tube,and demonstrate domain twisting at domain walls in ferroelectrics considering the flexoelectric effect.

    Isogeometric Analysis(IGA)-Based Topology Optimization for 3D Flexoelectric Structures

    Yao MengXiaoye YanWeisheng Zhang
    580-589页
    查看更多>>摘要:This paper presents isogeometric analysis(IGA)-based topology optimization for electrical performance of three-dimensional(3D)flexoelectric structures.IGA is employed to provide C1 continuity in shape function,which is required in treating high-order electromechanical coupling equations.To improve the computational efficiency in treating 3D problems,the redundant degrees of freedom removal technique is introduced.Regularization treatments are also implemented to avoid the numerical singularity induced by flexoelectricity.Both virtual loads and strain energy constraints are taken into consideration to prevent unexpected structural disconnection.Numerical examples and experiments on optimized structures demonstrate that the flexoelectric performance can be effectively improved using the proposed approach.

    Domain Engineering the Flexoelectric Response of BaTiO3-SrTiO3 Binary Films:A Phase Field Study

    Junyu TaoFan ZhangJianyuan ZhangWeijin Chen...
    590-597页
    查看更多>>摘要:The flexoelectric effect describes the interplay between material polarization and strain gradient.While much research has focused on control strategies for flexoelectricity,the impact of ferroelectric domain structure on the flexoelectric effect remains elusive.Through phase field simulations,we conduct a comparative study on the flexoelectric response of two types of BaTiO3-SrTiO3 binary films:BaTiO3-SrTiO3 multilayers and(Ba,Sr)TiO3 solid solutions.Our findings reveal that the flexoelectric response of these two systems,at the same Ba/Sr ratio,differs not only in magnitude but also in other aspects like temperature dependence,linearity,and hysteresis,due to their different ferroelectric domain structures and evolution dynamics.Our study deepens our current understanding of flexoelectricity in ferroelectrics and suggests"domain engineering"as a potential way to tailor this effect.

    Surface Elastic Effects on Electromechanical Responses of a Piezoelectric Semiconducting Nanobeam

    Aowen BaoXiaobao LiYuxue PuChunxiao Zhan...
    598-612页
    查看更多>>摘要:Piezoelectric semiconductors(PSCs)find extensive applications in modern smart electronic devices because of their dual properties of being piezoelectric and semiconductive.With the increasing demand for miniaturization of these devices,the performance of their components needs to be carefully designed and optimized,especially when reduced to nanosize.It has been shown that surface elastic properties play a substantial role in the mechanical performance of nanoscale materials and structures.Building on this understanding,the surface elastic effects,encompassing surface residual stress,surface membrane stiffness,and surface bending stiffness,are comprehensively taken into account to explore the electromechanical responses of a PSC nanobeam.Additionally,the flexoelectric effect on their responses is also systematically studied.The results of this work reveal that surface elastic properties predominantly influence mechanical performance,while the flexoelectric effect plays a more dominant role in electric-related quantities at the nanoscale.Notably,the significance of surface bending rigidity,which was often underestimated in the earlier literature,is demonstrated.Furthermore,owing to the flexoelectric effect,the linear distribution of electric potential and charge carriers along the length transforms into a nonlinear pattern.The distributions of electric potential and charge carriers across the cross section are also evidently impacted.Moreover,the size-dependent responses are evaluated.Our findings may provide valuable insights for optimizing electronic devices based on nanoscale PSCs.

    Bending Analysis of Circular Piezoelectric Semiconductor Plates Incorporating Flexoelectricity

    Liang SunZhengguang XiaoChunli ZhangWeiqiu Chen...
    613-621页
    查看更多>>摘要:Based on the three-dimensional(3D)basic equations of piezoelectric semiconductors(PSs),we establish a two-dimensional(2D)deformation-polarization-carrier coupling bending model for PS structures,taking flexoelectricity into consideration.The analytical solutions to classical flexure of a clamped circular PS thin plate are derived.With the derived analytical model,we numerically investigate the distributions of electromechanical fields and the concentration of electrons in the circular PS thin plate under an upward concentrated force.The effect of flexoelectricity on the multi-field coupling responses of the circular PS plate is studied.The obtained results provide theoretical guidance for the design of novel PS devices.